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Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters

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  • Gakkhar, Sunita
  • Singh, Brahampal

Abstract

A modified Leslie–Gower-type prey–predator model composed of a logistic prey with Holling’s type II functional response is studied. The axial point (1,0) is found to be globally asymptotically stable in a domain. Condition for stability of the non-trivial equilibrium point is obtained. The existence of stable limit cycle of the system is also established. The analysis for Hopf bifurcation is carried out. The numerical simulations are carried out to study the effects of seasonally varying parameters of the model. The system shows the rich dynamic behavior including bifurcation and chaos.

Suggested Citation

  • Gakkhar, Sunita & Singh, Brahampal, 2006. "Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1239-1255.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1239-1255
    DOI: 10.1016/j.chaos.2005.04.097
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    1. Gakkhar, Sunita & Singh, Brahampal, 2005. "Complex dynamic behavior in a food web consisting of two preys and a predator," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 789-801.
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    Cited by:

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    2. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    3. An, Xin-Lei & Yu, Jian-Ning & Chu, Yan-Dong & Zhang, Jian-Gang & Zhang, Li, 2009. "Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 865-873.
    4. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    5. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
    6. Zhang, Jian-Gang & Li, Xian-Feng & Chu, Yan-Dong & Yu, Jian-Ning & Chang, Ying-Xiang, 2009. "Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2150-2168.
    7. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    8. Gakkhar, Sunita & Sahani, Saroj Kumar, 2009. "A model for delayed effect of toxicant on resource-biomass system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 912-922.
    9. Wang, Xiaoqin & Wang, Weiming & Lin, Yezhi & Lin, Xiaolin, 2009. "The dynamical complexity of an impulsive Watt-type prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 731-744.
    10. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.

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